Which of the function below is that inverse of f(x)=x^-25

g⁻¹(x) = ±√(x + 25)

Step-by-step explanation:

g(x) = x² - 25     Rename g(x) as y

  y = x² - 25

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Solve for x  

        y = x² - 25          Add 25 to each side

y + 25 = x²                  Take the square root of each side

       x = ±√(y + 25)     Switch x and y

       y = ±√(x + 25)     Rename y as g inverse

g⁻¹(x) = ±√(x + 25)

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See the graphs of g(x) and g⁻¹(x) below.

g(x) is the red line. g⁻¹(x) is the purple line.

Each graph reflects the other about the dashed line representing the function y = x.